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From: David Roberts <droberts@maths.adelaide.edu.au>
To: Categories list <categories@mta.ca>
Subject: Strictifying monoidal functors
Date: Wed, 7 May 2008 16:29:08 +0930	[thread overview]
Message-ID: <E1JtitD-0000AH-Px@mailserv.mta.ca> (raw)

Hi all,

While we can make all monoidal categories strict, I was wondering how
strict we can make monoidal functors. More precisely, given a strong
monoidal functor F:(C,@,I) --> (D,*,1) between strict monoidal
categories, it has the data

m_xy: F(x)*F(y) ---> F(x@y)   (natural)

u:1 ---> F(I).

Is F naturally isomorphic to a strong monoidal functor such that u is
the identity?

In Baez-Lauda HDA 5 it is an exercise to the reader in the proof of
Proposition 8.3.6 to do this for weak monoidal categories.

Cheers,

David




                 reply	other threads:[~2008-05-07  6:59 UTC|newest]

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